簡約 (\sqrt[5]{t^2})/(\sqrt[6]{t^2)}

解

簡約

\frac{5 t ^{2}}{6 t ^{2}}

30 t^{2}

解答ステップ

\frac{5 t ^{2}}{6 t ^{2}}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

5 t^{2} = (t^{2})^{\frac{1}{5}}

= \frac{( t ^{2} ) ^{\frac{1}{5}}}{6 t ^{2}}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

6 t^{2} = (t^{2})^{\frac{1}{6}}

= \frac{( t ^{2} ) ^{\frac{1}{5}}}{( t ^{2} ) ^{\frac{1}{6}}}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= (t^{2})^{\frac{1}{5} - \frac{1}{6}}

結合

\frac{1}{5} - \frac{1}{6} : \frac{1}{30}

= 30 t^{2}